Statistical Questions

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Statistical Questions · Grade 6 · Worksheet 1

1. Is 'How many minutes do 6th graders spend on homework each night?' a statistical question? Explain why or why not. Answer: Yes, it is a statistical question because it anticipates variability in the responses. Solution: A statistical question is one that anticipates variability in the data used to answer it. Step 2: The question 'How many minutes do 6th graders spend on homework each night?' asks about a group (6th graders), not a single person.
   Full step-by-step solution

   Step 1: A statistical question is one that anticipates variability in the data used to answer it. Step 2: The question 'How many minutes do 6th graders spend on homework each night?' asks about a group (6th graders), not a single person. Step 3: Different 6th graders will have different amounts of homework time, so the answers will vary. Step 4: Because the question expects a variety of answers, it is a statistical question. The answer is: Yes, it is a statistical question.

2. A survey asked 1250 middle school students about their favorite type of book. The results showed that 28% preferred fantasy, 32% preferred mystery, 18% preferred science fiction, and the rest preferred historical fiction. How many students preferred historical fiction? Answer: 275 Solution: We know the total number of students is 1250. Fantasy: 28% Mystery: 32% Science Fiction: 18% Find the total percentage of the first three types. 28% + 32% + 18% = 78% Find the percentage for historical fiction.
   Full step-by-step solution

   Let's solve this step-by-step. Step 1: Understand the problem. We know the total number of students is 1250. The percentages for favorite book types are: Fantasy: 28% Mystery: 32% Science Fiction: 18% Historical Fiction: the rest Step 2: Find the total percentage of the first three types. 28% + 32% + 18% = 78% Step 3: Find the percentage for historical fiction. Since all students must add up to 100%, Historical Fiction = 100% - 78% = 22% Step 4: Calculate the number of students who preferred historical fiction. 22% of 1250 = (22/100) * 1250 Step 5: Perform the calculation. First, 22/100 = 0.22 Then, 0.22 * 1250 = 275 Step 6: Conclusion. So, the number of students who preferred historical fiction is 275.

3. Liam is tracking his reading progress for a school project. He recorded that he read for 45 minutes on Monday, 60 minutes on Tuesday, 30 minutes on Wednesday, 75 minutes on Thursday, and 50 minutes on Friday. What was the mean number of minutes Liam spent reading each day? Answer: 52 Solution: To find the mean number of minutes Liam spent reading each day, we need to calculate the average. The mean is found by adding up all the daily reading times and then dividing by the number of days. Monday: 45 minutes Tuesday: 60 minutes Wednesday: 30 minutes Thursday: 75 minutes Friday: 50…
   Full step-by-step solution

   To find the mean number of minutes Liam spent reading each day, we need to calculate the average. The mean is found by adding up all the daily reading times and then dividing by the number of days. Step 1: List the daily reading times. Monday: 45 minutes Tuesday: 60 minutes Wednesday: 30 minutes Thursday: 75 minutes Friday: 50 minutes Step 2: Add all the daily minutes together. 45 + 60 = 105 105 + 30 = 135 135 + 75 = 210 210 + 50 = 260 So, total minutes = 260. Step 3: Count the number of days. There are 5 days (Monday through Friday). Step 4: Divide the total minutes by the number of days. Mean = 260 / 5 Step 5: Perform the division. 260 ÷ 5 = 52 So, the mean number of minutes Liam spent reading each day is 52.

4. Kaia wants to know the typical height of students in her grade 6 class. She measures the height of every student in her class and records the data. Which of the following questions about her data is a statistical question, and why? Question A: How tall is the tallest student in the class? Question B: How tall are the students in the class? Answer: Question B is a statistical question because it anticipates variability in the heights of different students, while Question A has only one specific answer. Solution: A statistical question is one that anticipates variability in the data related to the question. Different students have different heights (e.g., 140 cm, 152 cm, 148 cm, etc.).
   Full step-by-step solution

   Step 1: Understand the definition of a statistical question. A statistical question is one that anticipates variability in the data related to the question. This means that if you ask the question to different people or about different subjects, you expect to get a range of different answers. Step 2: Analyze Question A: 'How tall is the tallest student in the class?' This question asks for a single, specific piece of information. There is only one tallest student, so the answer is a fixed number. There is no variability in the answer. Therefore, Question A is NOT a statistical question. Step 3: Analyze Question B: 'How tall are the students in the class?' This question asks about the heights of all students in the class. Different students have different heights (e.g., 140 cm, 152 cm, 148 cm, etc.). The answers would vary from student to student. Because the question anticipates this variability, it is a statistical question. Step 4: Conclusion. Question B is the statistical question because it expects a range of different heights, while Question A asks for a single, non-varying value.

5. A rectangular prism is drawn with a length of 12 cm, width of 8 cm, and height of 5 cm. If you were to calculate the volume of this prism, what would it be in cubic centimeters? Answer: 480 Solution: The formula for volume of a rectangular prism is length × width × height Substitute the given values: 12 cm × 8 cm × 5 cm First multiply 12 × 8 = 96 Then multiply 96 × 5 = 480 Include the units: 480 cubic centimeters The answer is 480.
   Full step-by-step solution

   Step 1: The formula for volume of a rectangular prism is length × width × height Step 2: Substitute the given values: 12 cm × 8 cm × 5 cm Step 3: First multiply 12 × 8 = 96 Step 4: Then multiply 96 × 5 = 480 Step 5: Include the units: 480 cubic centimeters The answer is 480.

6. Which question is statistical: 'How many books does Emma read in a month?' or 'How many books does Emma read in 2025?' Explain why. Answer: 'How many books does Emma read in a month?' is statistical because the number can vary each month. Solution: Identify the two questions. Question 1: 'How many books does Emma read in a month?' Question 2: 'How many books does Emma read in 2025?' Consider variability.
   Full step-by-step solution

   Step 1: Identify the two questions. Question 1: 'How many books does Emma read in a month?' Question 2: 'How many books does Emma read in 2025?' Step 2: Consider variability. For Question 1, the number of books Emma reads can change from month to month (e.g., 2 books in January, 5 in February, 0 in March). This shows variability, so it is a statistical question. Step 3: For Question 2, the year 2025 is a fixed time period. The number of books Emma reads in that specific year is a single, fixed number (once the year is over). There is no variability in the answer because it refers to one specific time frame. So it is not a statistical question. Step 4: Conclusion: 'How many books does Emma read in a month?' is the statistical question because the answer can vary from month to month.